Perturbative-Integro-Differential Solution for the Nonlinear Hydraulic Diffusivity Equation for Compaction Damage Management in Poroelastic Stress-Sensitive Oil Reservoirs

Abstract

Abstract Considering the effects of poroelasticity in oil flow models becomes the modeling regarding formation evaluation and reservoir engineering more realistic. It occurs because poroelastic parameters, e.g., in situ overburden stress, σob, Young's modulus, E and Biot's coefficient, α have a fundamental role in reservoir depletion response. This paper develops a new perturbative solution for the nonlinear hydraulic diffusivity equation (NHDE) in Biot's effective stress-sensitive infinite-acting-oil reservoirs. For this modeling, the NHDE is perturbed until the first-order using the dimensionless inverse Biot effective stress-dependent permeability, 1/kD (σ′) as a perturbation parameter, ∈. A new stress-sensitive function, m(σ′), that couples geomechanics to the transient permeability change is presented, and the mathematical formulation is developed in terms of this function. The solution shows that the phenomenon of permeability loss over the production curve is composed of the linear solution pD(tD) = − (α/2)Ei(−1/4tD) plus a nonlinear term that results in permeability change caused by pressure drop inside the reservoir pores. In addition, the pseudo-pressure derivative is used to compute the instantaneous permeability loss using the fact that ∂mD/∂tD = kD(σ′)∂pD/∂tD. The findings of this study allowed us to notice the role of the aforementioned poroelastic parameters in permeability change during oil production.